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Simplifying (3x2 + 2x + 5) + (3x2 + 4x + 3) = 0 Reorder the terms: (5 + 2x + 3x2) + (3x2 + 4x + 3) = 0 Remove parenthesis around (5 + 2x + 3x2) 5 + 2x + 3x2 + (3x2 + 4x + 3) = 0 Reorder the terms: 5 + 2x + 3x2 + (3 + 4x + 3x2) = 0 Remove parenthesis around (3 + 4x + 3x2) 5 + 2x + 3x2 + 3 + 4x + 3x2 = 0 Reorder the terms: 5 + 3 + 2x + 4x + 3x2 + 3x2 = 0 Combine like terms: 5 + 3 = 8 8 + 2x + 4x + 3x2 + 3x2 = 0 Combine like terms: 2x + 4x = 6x 8 + 6x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 8 + 6x + 6x2 = 0 Solving 8 + 6x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 3x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 3x2 = 0 Solving 4 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + x + x2 = 0 + -1.333333333 x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 x + x2 = -1.333333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -1.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.333333333 + 0.25 Combine like terms: -1.333333333 + 0.25 = -1.083333333 1.25 + x2 = -1.083333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.083333333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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